GEOMETRIC OPTICS AND CONVEX FUNCTIONS IN THE BOUNDARY CONTROL OF THE WAVE EQUATION

We seek to control the solution to a hyperbolic equation in a cylindrical domain by prescribing Dirichlet conditions on some part of the lateral boundary of the domain. We give a new argument, based on geometric optics, for a theorem on control given a convex function, which Lasiecka, Triggiani and Yao have shown via Carleman estimates. We also give an example of a space where control is guaranteed by geometric optics, but no convex function exists.